Period

• One cycle of a sinusoid is $2\pi$ radians.
• The period $T$ of a sinusoid is the time (in seconds) it takes to complete one cycle.

  Figure 2: Sinusoid.

  

• Since sinusoids are periodic with period $2\pi$, an initial phase of $\phi$ is indistinguishable from an initial phase of $\phi \pm 2\pi$.
• We may therefore restrict the range of $\phi$ so that it does not exceed $2\pi$. Typically we choose the range
  $$-\pi < \phi < \pi,$$
  but we many also encounter
  $$0 < \phi < 2\pi.$$